# Area of a Sector

A **sector** is a portion of a circle bounded by two radii and the arc joining their extremities. It is thus a form of a triangle with a covered base. In the figure, the portion is a sector. Arc is called the **arc of the sector** and is called the **angle of the sector**.

The area of a sector of a circle is equal to a fraction of the area of the circle determined by dividing the size of the angle by . So, if the angle of the sector is , the area of the sector is or the area of the circle. Thus, the area of a sector of the circle divided by the area of the whole circle is proportional to the angle of the sector divided by .

If the angle is given in degrees, say, then

Area of the sector:

Length of the arc:

If the angle is given in radians, say radians, then

Area of the sector,

If the length of the arc and the radius of the circle are given, then

Area of the sector, where

__Example__:

Find the area of a sector of in a circle of radius cm.

__Solution__:

The sector has angle .

Its area is equal to

Since the radius cm

Therefore square

__Example__:

The minute hand of a clock is cw long. Find the area which is described on the clock face between A.M to A.M.

__Solution__:

Given that the length of the minute hand's radius is cm

minutes

minutes

Since the area of sector

square cm